Question: Given $ m \angle QPR = 5x + 25$, and $ m \angle RPS = 9x - 41$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Solution: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 25} + {9x - 41} = {180}$ Combine like terms: $ 14x - 16 = 180$ Add $16$ to both sides: $ 14x = 196$ Divide both sides by $14$ to find $x$ $ x = 14$ Substitute $14$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 9({14}) - 41$ Simplify: $ {m\angle RPS = 126 - 41}$ So ${m\angle RPS = 85}$.